Decidability and Completeness in Real-Time Processes

Liang Chen

Abstract: By extending Milner's CCS with time, a general
interleaving model for real-time systems is proposed. We make no
assumption about the underlying nature of time and allow time to be
discrete (such as the integers) or dense (such as the rationals or
the reals). Time variables allow us to represent the notion of time
dependency and in general the language is more expressive than
those without time variables. We extend the notion of bisimulation
to timed processes and show that strong equivalence is still
decidable. Decidability is independent of the choice of time
domain. Also we present a proof system in which there are no
infinite proof rules. Again the proof system is independent of the
choice of time domain. We show that the proof system is complete
over dense time domains, but only complete for some subclass of
processes over discrete time domains.